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POSITIVE DEFINITE TOEPLITZ COMPLETIONS

Published online by Cambridge University Press:  01 April 1999

CHARLES R. JOHNSON ,
MICHAEL LUNDQUIST  and
GEIR NÆDAL
CHARLES R. JOHNSON
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23185, USA
MICHAEL LUNDQUIST
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA
GEIR NÆDAL
Affiliation:
Department of Engineering, Stord/Haugesund College, Skåregt. 103, N-5500 Haugesund, Norway Current address: RF-Rogaland Research, Thormøhlensgt. 55, N-5008 Bergen, Norway
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Abstract

The problem of completing a partially prescribed Toeplitz matrix to a positive definite Toeplitz matrix is considered. The main result is a characterization of the patterns of specified entries that guarantee the existence of a positive definite Toeplitz completion of a partial positive definite Toeplitz matrix. This characterization resolves affirmatively a conjecture of C. R. Johnson and L. Rodman.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 507 - 520
Copyright
The London Mathematical Society 1999

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